The story I'm getting is that it barely appears before the LXX, and the NT seems to introduce a new usage (in place of other words for love).

BDAG wrote:this term has left little trace in polytheistic Gk. lit. ... Its paucity in gener. Gk. lit. may be due to a presumed colloq. flavor of the noun

Nygren wrote:the double spell cast upon us by tradition and language is broken as soon as we realise that Eros and Agape have originally nothing whatever to do with one another

(Really, nothing? Perhaps nothing except semantic domain overlap?)

Leon Morris wrote:You can find it a few times in the Old Testament, where as a matter of fact it seems to mean pretty much what eros means; it seems as if when the translators of the Old Testament into Greek came up against a word for romantic love they avoided eros because of some of the associations it had in the areas in which they lived, and so they used another word, and they dug up agape. It's used in one or two writers with a biblical slant, and that's it. It is not found in the whole, vast range of Greek literature before the New Testament, other than just these few, odd places. But in the New Testament, it is the characteristic word for love. If you come up against the noun 'love' in your translation of the New Testament, it is a stone cold certainty that the Greek is 'agape.' That is the one word that the New Testament writers use for love.

Moulton+Milligan in 1930 wrote:Ἀγάπη is in any case a back-formation from the verb, replacing the older ἀγάπησις, and originating doubtless in a restricted dialectic area.

Moulton & Milligan have your answer there. It's a back formation from the verb ἀγαπάω. At the point of the LXX it was a recent coinage--if you look at LSJ, you'll see the LXX is the first entry. LSJ orders citations by date, so you know that everything that comes after the first citation is equal in age or newer.

Now...if you want information about its etymology, you can go to the etymology ἀγαπάω--*αγα is a old Greek intensifying prefix and the root *πα likely meant something like 'protect' in the context of similar Sanskrit formations and the Greek verb ἐμπάζομαι. The reconstructed IE root is *peh2. That's all from Beekes (2010), but the reconstruction isn't viewed as confident.